Using multiple imputation and intervention-based scenarios to project the mobility of older adults

Background Projections of the development of mobility limitations of older adults are needed for evidence-based policy making. The aim of this study was to generate projections of mobility limitations among older people in the United States, England, and Finland. Methods We applied multiple imputation modelling with bootstrapping to generate projections of stair climbing and walking limitations until 2026. A physical activity intervention producing a beneficial effect on self-reported activities of daily living measures was identified in a comprehensive literature search and incorporated in the scenarios used in the projections. We utilised the harmonised longitudinal survey data from the Ageing Trajectories of Health – Longitudinal Opportunities and Synergies (ATHLOS) project (N = 24,982). Results Based on the scenarios from 2012 to 2026, the prevalence of walking limitations will decrease from 9.4 to 6.4%. A physical activity intervention would decrease the prevalence of stair climbing limitations compared with no intervention from 28.9 to 18.9% between 2012 and 2026. Conclusions A physical activity intervention implemented on older population seems to have a positive effect on maintaining mobility in the future. Our method provides an interesting option for generating projections by incorporating intervention-based scenarios. Supplementary Information The online version contains supplementary material available at 10.1186/s12877-022-03008-4.


Supplementary Material
Kontto J, Paalanen L, Sund R, Sainio P, Koskinen S, Demakakos P, Tolonen H, Härkänen T: Using multiple imputation and intervention-based scenarios to project the mobility of older adults  Table S1 12 o Supplementary Fig. S2 13 o Supplementary Table S2 14 -Transition probabilities between 2010 and 2012 15 o Supplementary Table S3 16 -R-code for generating projections 17 -References 25 Literature review on RCT results: search strategy Medline OVID 18 April 2019 1 "*Aged, 80 and over"/ or *Aged/ (17151) 2 (elderly or ageing or aging or "old population*" or "older population* older citizen*" or "older adult*").ti. (204750) 3 1 or 2 (213723) 4 "Systematic Review"/ (104632) 5 (systematic review or meta-analysis).pt. (161843) 6 4 or 5 (161843) 7 "Activities of Daily Living"/ or "Quality of life"/ or "mental competency"/ or cognition/ or autonomy/ or "independent living"/ or exp "Health Behavior"/ or "Health Risk Behavior"/ or Risk Reduction Behavior/ or "Physical Fitness"/ or Muscle Strength/ or "Health status"/ or "social capital"/ or "International Classification of Functioning, Disability and Health"/ or "Community Participation"/ or "Social Participation"/ or exp Health Behavior/ or Personal Satisfaction/ or Social Networking/ or Sedentary behavior/ or Adaptation, Psychological/ or Social Support/ or Mental Health/ or Lifestyle/ or Healthy Lifestyle/ (876298) 8 (function* or cognitive or cognition or independen* or autonomy or mobility or "physical activity" or "physical health" or "health status" or "muscle strength" or fitness or inactiv* or sedentary or "successful ageing" or "successful aging" or "healthy aging" or "healthy ageing" or "healthy living" or "health habits" or "quality of life" or "activities of daily living" or "social capacity" or "health behavi*r" or engag* or participat* or "social networks" or "social life" or satisfactory or satisfaction ot coping or capability or capacity or psychosocial or "social network*" or "risk reduction" or lifestyle).ti. (1167801) 9 7 or 8 (1851444) 10 (intervention* or therap* or treatment* or treated or program* or policy or policies or tool* or device* or technique* or training or coaching or counsel* or education or prevention or preventive or "health promotion" or "clinical trial*" or "clinical stud*" or rct* or random*).ti,ab,sh. (10385025) 11 (benefit* or promot* or effect* or efficacy or impact* or outcome* or improve* or increas* or decreas*).ti.
12 10 or 11 (11972623) 13 3 and 6 and 9 and 12 (597) The search yielded 597 results. After crude selection by the information specialist 172 articles remained. Of these, 16 articles with outcome related to physical functioning were selected for further evaluation based on the estimated applicability to ATHLOS. For example, reviews with too specific interventions such as yoga or aquatic exercise were excluded, as well as reviews including interventions amongst a homogenous study population such as only obese participants.
Other functional limitation outcomes: vision, memory, and hearing limitations In our study, we selected outcomes representing different dimensions of functional ability. In order to define one set of dimensions, we utilized the results by Caballero et al. [1] who developed a health metric in the ATHLOS project. In their procedure, 45 items related to functioning, and available in the ELSA baseline data, were assessed with exploratory factor analysis. As a result, five factors were identified representing the following dimensions of functioning: mobility, eyesight, cognitive functioning, psychological functioning, and hearing. In addition to two items from mobility factor, we selected an item with the highest loading from each other dimensions of functioning as outcomes with one precondition: the item is available in all three studies (HRS, ELSA, H2000). The highest loading of items of the psychological functioning factor was 0.54 so no outcome was selected from that factor. As a result, three functional limitations were selected as outcomes: 1) Limitations in near vision after correction with glasses; 2) Limitations in delayed recall; and 3) Limitations in hearing. The selected outcomes were based on self-reported information, except memory limitations, where delayed recall test with ten words was used. Those who recalled less than five words out of ten immediately after three rounds of learning the words were defined as having limitations in short-term memory [2].

The preparation of data and imputation of missing values
A bootstrap sample is in wide format, in which all observed data of both the outcomes and predictors of an individual are on the same row, and denoted by = ( 1 , … , ), where waves 1, … , correspond the years 2000-2012 biennially.
We simplify the notation by omitting indices relating to individuals. In order to have compatible years across studies, the participants of the Health 2011 Survey were randomly assigned into 2010 and 2012.
Multiple imputation based on chained equations and classification and regression tree (CART) [3,4] was implemented to impute the missing values of using the package 'mice' of the R software [5]. Since the number of variables in was 183 (26 variables across 7 waves in addition to time-independent variable study), the complexity parameter value (cp) in function 'rpart' was set to 0.001 and the minimum number of observations in any terminal node (minbucket) was set to 100 to reduce the number of predictors in the imputation models for each variable [6].
Here, we assumed that the projections for wave + could depend only on , . . . , + −1 as consisted of waves: These distributions could be formulated using the predictive distributions of Bayesian inference: The imputed values approximated the Bayesian predictive distributions which is a proper imputation method, as the different sources of uncertainty (parameter, model and prediction uncertainties) are accounted for [8,9]. CART can adapt to possible interactions and non-linearities of the variables.

Results for vision, memory, and hearing limitations Selection of predictors
For vision, memory, and hearing limitations all previous measurements were among selected predictors (Supplementary   Table S1). IADL score in 2012 (48%) and ADL score in 2012 (13%)

Transition probabilities between 2010 and 2012
Since the most important predictor of all outcomes was the previous measurements of the corresponding outcome, we present the transition probabilities of outcomes between 2010 and 2012. In general, the transition probabilities in HRS and ELSA were similar, whereas several probabilities of H2000 differed from the probabilities of the two other studies (Supplementary Table S3 whereas in HRS and ELSA the probabilities were 44% and 43%, respectively.

Difficulties in vision or hearing
The probabilities were similar across studies. Among those who survived until 2012, the probability of those who recovered from difficulties in vision varied between 39% and 43% across studies, while 11% to 14% developed difficulties in vision. Correspondingly for difficulties in hearing, 23% to 29% recovered and 16% to 20% developed difficulties across studies.